The gravitational structure of the proton The pressure Th A new - PowerPoint PPT Presentation

The gravitational structure of the proton The pressure Th A new direction of distribution di experimental hadron inside th the physics pr prot oton on Volker D. Burkert Jefferson Laboratory V.B., L. Elouadrhiri, F.X. Girod Nature 557 (2018) no.7705, 396-399 4/10/19 1

Gravitational waves observed Gravity governs movements of massive structures in the universe. • Plays a decisive role in neutron stars leading to the most densely • packed macroscopic objects in the universe. The merger of two neutron stars generated gravitational waves that told us much about the equation-of-state of the neutron stars themselves. Can we use gravitational waves to probe the interior of the proton and the distribution of the strong force? 4/10/19 2 2

The strong interaction is born Crossover from the QGP phase to the hadron phase occurs just micro- seconds after the Big Bang - chiral symmetry is broken - quarks acquire dynamical mass - confinement becomes manifest Hadrons (ground state or excited) emerge during this “cross over” period. The proton emerges as the most fundamental bound-state in nature. It is the most suitable object to study the intrinsic forces. 3

Probing properties of the proton The structure of strongly interacting particles can be probed by means of the other fundamental forces: electromagnetic, weak, and gravity . Vector Tensor Electro- Gravity magnetism Q p µ p M p J p D p PCAC g A g P Weak interaction 4/10/19 4 4

Fundamental properties of the proton vector axial tensor The PDG edition of 2018 does not have an entry for the D -term The D -term is the last unknown fundamental global property of the proton How can we obtain any information about this property of the proton? 5

Gravitational properties of the proton? Gravitational Interaction of Fermions Yu. Kobzarev and L.B. Okun, JETP 16, 5 (1963) Energy-Momentum Structure Form Factors of Particles H. Pagels, Phys. Rev. 144 (1966) 1250-1260 “….. , there is very little hope of learning anything about the detailed mechanical structure of a particle, because of the extreme weakness of the gravitational interaction” ( H. Pagels) 6

Generalized Parton Distributions (GPDs) D. Müller et al., F. Phys. 42,1994 X. Ji, PRL 78, 610, 1997 A. Radyushkin, PLB 380, 1996 Deeply virtual Compton scattering p G G p => p J=2 p x B x = hard scattering 2 - x B p factorization γ soft part J=2 γγp => p γ v p p p As the e.m. coupling is many orders of magnitude stronger than gravitation makes the DVCS process accessible in experiments. 7

GPDs – GFFs Relations Proton matrix element of the Energy-Momentum Tensor contains three gravitational form factors (GFF) and can be written as: M 2 (t) : Mass/energy distribution inside the nucleon J (t) : Angular momentum distribution d 1 (t) : Forces and pressure distribution X. Ji, Phys. Rev. D55, 7114 (1997) GPDs not directly measurable from available DVCS data alone • gra 8

GPDs & Compton Form Factors (CFF) We can determine the Compton Form Factor H ( ξ, t ) through an • integral over the quark longitudinal momentum fraction x . Polarized beam: DVCS BH Ds LU ~ Im {F 1 H ( x , t )+...} Unpolarized beam: d s U /dx B dt ~ {Re H ( x , t )+…} d 1 (t) H (ξ,t ) First suggestion to determine pressure and shear forces in hard exclusive processes. 9

The CLAS Detector (JLab) In operation from 1997 to 2012 ü Large acceptance ü Good resolution ü Particle identification 10

DVCS Beam Spin Asymmetry F.X. Girod et al. Phys.Rev.Lett. 100 162002 (2008) Measurements in a large phase space Q 2 , x B , t small & suppressed 11

DVCS Unpolarized Cross-Sections H.S. Jo et al., Phys.Rev.Lett. 115 (2015 ) 12

Extract CFF H ( x , t ) in Fits Direct method: Extract CFF H H directly in all x and t bins from the data Fit global parameterization of BSA to determine Im H Step: 1 Step: 2 Fit differential DVCS cross sections to determine Re H K. Kumericki, D. Müller, Nucl. Phys. B 841, 1-58, 2010 D. Müller, T. Lautenschlager, K, Passek-Kumericki, G. Schaefer, Nucl.B. 884, 438, 2014 Use subtracted fixed-t dispersion relation to determine D ( t ) Step: 3 M. Polyakov: conjecture that subtraction term is related to the gravitational form factor D Q (t) I.V. Anikin and O.V. Teryaev, Phys.Rev.D76, 056007 (2007) M. Diehl and D.Y. Ivanov, Eur. Phys. J. C52, 919, (2007) 13

Fits to determine H( H( x , , t ) ) and D ( t ) Samples of differential cross sections with fits Samples of Beam Spin Asymmetry with fits DVCS - BSA F.X. Girod et al., Phys.Rev.Lett. 100 (2008) 162002 ; H.S. Jo et al., Phys.Rev.Lett. 115 (2015) 212003 14

Extraction of Compton Form Factor H( ξ ,t ,t) Data point closest to t=0 D(t)=0 From KM10 parameterization Markers: Determination from beam asymmetry and unpolarized cross section. Curves: Using KM10 parameterization. Bands from estimates of contributions from other GPDs. 4/10/19 15 15

Extraction of Compton Form Factor H (ξ,t) -t=0.26GeV 2 -t=0.11GeV 2 -t=0.34GeV 2 -t=0.15GeV 2 The Real and Imaginary parts of Compton Form H ( ξ ,t) for different ξ and t values, resulting from the fit to the BSA and cross section data. -t=0.20GeV 2 16

Extraction of D( t ) for quark distribution D(t) from CLAS 6 GeV data D Q (0) = -1.47 ± 0.10 ± 0.22 M 2 = 1.06 ± 0.10 ± 0.15 α = 2.76 ± 0.25 ± 0.50 D Q (0) < 0 This is a critical results, required for dynamical stability of the proton. systematic uncertainties Deeply rooted in chiral symmetry breaking. First determination of the proton’s D-term D(0), and its form factor D(t). 4/10/19 17 17

Comparison of D Q (t) with theory M. Polyakov, P. Schweitzer, Int.J.Mod.Phys. A33 (2018 ) • Chiral Quark Soliton Model • Dispersion Relations, normalized at t=0 . • Lattice QCD LHPC, no disconn. diag. D Q (t) • Global fit – K.L.M. EPJ A52 (2016) 6 , 157 Global properties of the Proton -1.47 (10) (22 ) 18

d 1 ( t ) - Gravitational Form Factor M.V. Polyakov and C. Weiss, Phys.Rev.D60, 114017 (1999) Expansion in Gegenbauer polynomials d 1 ( t ) = 25/18 D ( t ) (From model estimates next order term d 3 << d 1 ) V.B., L. Elouadrhiri, F.X. Girod Nature 557 (2018) no.7705, 396-399 d 1 (0) < 0 dynamical stability of bound state 19

Pressure distribution inside the proton M.V. Polyakov, Phys. Lett. B555 (2003) 57 Data before CLAS CLAS data CLAS12 proj. d 1g = d 1q Repulsive pressure near center p(r=0) ~ 10 35 Pa Confining pressure at r > 0.6 fm Atmospheric pressure: 10 5 Pa Pressure in the center of neutron stars ~ 10 34 Pa von Laue condition: ∫ r 2 p(r)dr = 0 V.B., L. Elouadrhiri, F.X. Girod Nature 557 (2018) no.7705, 396-399 verified within uncertainties 20

Comparison with χQSM • Gravitational form factors have been computed in Lattice QCD and various models. K. Goeke et al, Phys.Rev. D75 (2007) 094021 World data CLAS data χQSM CLAS12 proj . r 2 p(r) (GeV fm -1 ) d 1g = d 1q Similar p(r) dependence In the χQSM the pion field provides the confining pressure at the proton’s periphery . 21

CLAS12 @ JLab Readout channels: 110,000 Luminosity: 10 35 cm -2 s -1 Data acquisition: 800Mb/s 22 22

Summary and Outlook ­ First determination of a mechanical property of the proton opens a new perspective on experimental hadron physics ­ It puts limits on the last unknown global property of the proton ­ It gives access the partonic energy momentum tensor and opens a new avenue to test confinement mechanism ­ A flurry of theory papers appeared following the publication in Nature. ­ This is an exciting time at the beginning of the 12 GeV high precision era at Jefferson Lab. ­ It will be an essential part of the EIC program as well, to measure the gluon contributions to the EMT. 23

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Some papers following the Nature paper Hadron tomography in meson-pair production and gravitational form factors • S. Kumano, Qin-Tao Song, O.V. Teryaev, arXiv:1902.04333 Probing gravity at sub-femtometer scales through the pressure distribution inside the proton • P.P. Avelino, arXiv:1902.01318 Gravitational form factors within light-cone sum rules at leading order , I.V. Anikin, arXiv:1902.00094 • Bounds on the Equation of State of Neutron Stars from High Energy Deeply Virtual Exclusive • Experiments, S. Liuti, A. Rajan, K. Yagi, arXiv:1812.01479 Revisiting the mechanical properties of the nucleon , C. Lorcé , H. Moutarde, A. P. Trawiński, • Eur.Phys.J. C79 (2019) no.1, 89 Pressure Distribution and Shear Forces inside the Proton , P. E. Shanahan, W. Detmold, Phys.Rev.Lett. • 122 (2019) Gluon gravitational form factors of the nucleon and the pion from lattice QCD, P. E. Shanahan, W. • Detmold, Phys.Rev. D99 (2019) no.1, 014511 Nucleon gravitational form factors from instantons : forces between quark and gluon subsystems, M. • Polyakov, H.-D. Son, JHEP 1809, JHEP 2018. Operator relations for gravitational form factors of a spin-0 hadron , Kazuhiro Tanaka, Phys.Rev. D98 • (2018) Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, M. Polyakov, P. • Schweitzer, Int.J.Mod.Phys.A33 (2018) On the desert between neutron star and black hole remnants , R. Caimmi, Appl. Math. Sci. 2018 • 4/10/19 25 25